So now we have the clear problem.

Why are they lying, and what is the truth which they are trying so hard to conceal?
Let us try, Watson, you and I, if we can get behind the lie and reconstruct the truth.
"How do I know that they are lying?
Because it is a clumsy fabrication which simply could not be true.

Consider! According to the story given to us, the assassin had less than a minute after the murder had been committed to take that ring, which was under another ring, from the dead man's finger, to replace the other ring--a thing which he would surely never have done--and to put that singular card beside his victim.

I say that this was obviously impossible.
"You may argue--but I have too much respect for your judgment, Watson, to think that you will do so--that the ring may have been taken before the man was killed.

The fact that the candle had been lit only a short time shows that there had been no lengthy interview.